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NASA NTRS1984

An assessment of the accuracy of orthotropic photoelasticity - Abbreviated report

A brief overview is presented of a comprehensive study whose aim was to assess the accuracy of orthotropic photoelasticity. Particular attention is given to calibration of the material, forward testing for global and local behavior, and backward testing for stress determination. The experimentally determined stresses were found to agree with the elasticity solution. It is concluded that orthotropic photoelasticity does not appear to have the resolution of its isotropic counterpart, this being a consequence of the inherent inhomogeneity of the material.

Hyer, M. W.↗

NASA NTRS1986

Subset Regression

Backward elimination procedure minimizes prediction errors of equations fitted to factorial experiments. Problem of minimizing prediction error solved for two-level full- or fractional-factorial experiment with 16 factorial points and 0 to 6 center points. Such experiment provides 16 orthogonal coefficient estimates for empirical polynomial model. Each coefficient estimated with low variance error estimated from 16 observations.

Holms, A. G.↗

NASA NTRS1984

Accelerated convergence for incompressible flow calculations

Two improved algorithms which solve the steady-state Navier-Stokes equations, PISO and SIMPLER, are studied. Computations were carried out on progressively finer grids for the driven cavity and flow over a backward-facing step. The effects of relaxation factor, number of grid nodes and number of sweeps through the pressure equations are studied to evaluate the performance of the PISO and SIMPLER schemes. Results show that these improved schemes accelerate the convergence rate of the solution generally by a factor of two as compared to the SIMPLE method.

Neely, G. M.↗

NASA NTRS1984

Transformation of two and three-dimensional regions by elliptic systems

The research during this period continued to expand the class of numerical algorithms that can be accurately and efficiently implemented on overlapping grids. Whereas previous calculations have been used to solve elliptic equations and to find the steady-state solution of parabolic equations, the present work is aimed towards developing time-accurate solution techniques for parabolic and hyperbolic equations. The primary difficulty here is in the correct treatment of the interior boundary nodes that must be updated at each iteration. The implementation of explicit methods is straightforward. However, the common practice of lagging these values when using an implicit methods leads to inconsistencies in the difference equation. One way to avoid this problem is to alternately calculate with an implicit and an explicit method on each subgrid. With this procedure, the explicit method generates boundary values at the next time level which are then used by the implicit step. It can be shown that when a backward implicit method is combined with a forward explicit method, the composite method is second order accurate and unconditionally stable for linear problems. A second area in which progress can be reported is in the distribution of grid points on curves and surfaces.

Mastin, E. W.↗

NASA NTRS1984

A numerical investigation of planetesimal collision trajectories with a Moon accumulating in Earth orbit

In the scenario of lunar origin in which the Moon is assumed to have accreted most of its mass while in orbit about the Earth, ismals on the accrea knowledge of the relative impact rates of heliocentric planetting Earth and Moon is essential for any attempt to establish dynamical constraints on lunar origin. Numerical integrations of the regularized equations of motion for four bodies (Sun, Earth, Moon, planetismal) were done. A planetismal impact trajectory was calculated by assuming that the planetismal has hit the surface of the Moon at an assumed location, traveling in an assumed direction, and with an assumed impact speed. Next, the equations of motion were numerically integrated backward in time in order to determine from where the planetismal has come. In this way those volumes in heliocentric orbital element space which contribute trajectories that directly impact the Moon.

Cox, L. P.↗

NASA NTRS1985

Hydrodynamic stability problem formulated by numerical solutions of the Navier-Stokes equations

The problem of hydrodynamic stability and the transition from laminar to turbulent flows are reformulated by seeking numerical solutions of the full, unapproximated Navier-Stokes equations. This method differs significantly from the well known Orr-Sommerfeld equation approach. The oncoming laminar flow is disturbed by forced, time dependent perturbations. The magnitudes of these perturbations are arbitrary. Then, the ensuing spatial and temporal development of the imposed perturbations on the basic flow is calculated by direct numerical solutions of the time dependent Navier-Stokes equations. One of the main advantages of this method is its ability to simulate nonlinear processes. As a specific application of this technique to SSME (Space Shuttle Main Engine) flow configurations, computer programs have been written for the two dimensional flow over a backward facing step. This numerical code will be tested for operational use as part of a continued research collaboration effort with the NASA/MSFC counterparts.

Hyun, J. M.↗

NASA NTRS1985

Structural response of a rotating bladed disk to rotor whirl

A set of high speed rotating whirl experiments were performed in the vacuum of the MIT Blowdown Compressor Facility on the MIT Aeroelastic Rotor, which is structurally typical of a modern high bypass ratio turbofan stage. These tests identified the natural frequencies of whirl of the rotor system by forcing its response using an electromagnetic shaker whirl excitation system. The excitation was slowly swept in frequency at constant amplitude for several constant rotor speeds in both a forward and backward whirl direction. The natural frequencies of whirl determined by these experiments were compared to those predicted by an analytical 6 DOF model of a flexible blade-rigid disk-flexible shaft rotor. The model is also presented in terms of nondimensional parameters in order to assess the importance of the interation between the bladed disk dynamics and the shaft-disk dynamics. The correlation between the experimental and predicted natural frequencies is reasonable, given the uncertainty involved in determining the stiffness parameters of the system.

Crawley, E. F.↗

NASA NTRS1983

Optimal design and use of retry in fault tolerant real-time computer systems

A new method to determin an optimal retry policy and for use in retry of fault characterization is presented. An optimal retry policy for a given fault characteristic, which determines the maximum allowable retry durations to minimize the total task completion time was derived. The combined fault characterization and retry decision, in which the characteristics of fault are estimated simultaneously with the determination of the optimal retry policy were carried out. Two solution approaches were developed, one based on the point estimation and the other on the Bayes sequential decision. The maximum likelihood estimators are used for the first approach, and the backward induction for testing hypotheses in the second approach. Numerical examples in which all the durations associated with faults have monotone hazard functions, e.g., exponential, Weibull and gamma distributions are presented. These are standard distributions commonly used for modeling analysis and faults.

Lee, Y. H.↗

NASA NTRS1985

An implicit finite-difference code for a two-equation turbulence model for three-dimensional flows

An implicit finite difference code was developed which solves the transport equations for the turbulence kinetic energy and its dissipation rate in generalized coordinates in three dimensions. The finite difference equations are solved using the Beam-Warming algorithm. The kinetic energy-dissipation code, KEM, provides the closure; i.e., the turbulent viscosity for calculation of either compressible or incompressible flows. Turbulent internal flow over a backward-facing step has been calculated using the present code in conjunction with the Incompressible Navier-Stokes Code, INS3D. The results are in good agreement with experiments and two dimensional computations of other researchers.

Kaul, U. K.↗

NASA NTRS1985

Particle acceleration due to shocks in the interplanetary field: High time resolution data and simulation results

Data were examined from two experiments aboard the Explorer 50 (IMP 8) spacecraft. The Johns Hopkins University/Applied Lab Charged Particle Measurement Experiment (CPME) provides 10.12 second resolution ion and electron count rates as well as 5.5 minute or longer averages of the same, with data sampled in the ecliptic plane. The high time resolution of the data allows for an explicit, point by point, merging of the magnetic field and particle data and thus a close examination of the pre- and post-shock conditions and particle fluxes associated with large angle oblique shocks in the interplanetary field. A computer simulation has been developed wherein sample particle trajectories, taken from observed fluxes, are allowed to interact with a planar shock either forward or backward in time. One event, the 1974 Day 312 shock, is examined in detail.

Kessel, R. L.↗

NASA NTRS1985

Spatial distribution of cosmic rays in magnetic cycles of the Sun

The space-time distribution of cosmic ray (CR) density is determined from the solution of the anisotropic diffusion equation. The boundary problem is solved in a quasistationary axisymmetric case, taking into account the delay of cosmic rays relative to the cyclic variations of solar activity. The specificty of the modulation model is the use of the empirical dependence of the free path of particles for scattering on the observed latitudinal distribution of solar activity. Another specific feature of the model is an account of an additional effect due to the drift of charged particles towards the helio-equator plane or backward, depending on the direction of the total magnetic field of the Sun.

Alania, M. V.↗

NASA NTRS1985

Single particle momentum and angular distributions in hadron-hadron collisions at ultrahigh energies

The forward-backward charged multiplicity distribution (P n sub F, n sub B) of events in the 540 GeV antiproton-proton collider has been extensively studied by the UA5 Collaboration. It was pointed out that the distribution with respect to n = n sub F + n sub B satisfies approximate KNO scaling and that with respect to Z = n sub F - n sub B is binomial. The geometrical model of hadron-hadron collision interprets the large multiplicity fluctuation as due to the widely different nature of collisions at different impact parameters b. For a single impact parameter b, the collision in the geometrical model should exhibit stochastic behavior. This separation of the stochastic and nonstochastic (KNO) aspects of multiparticle production processes gives conceptually a lucid and attractive picture of such collisions, leading to the concept of partition temperature T sub p and the single particle momentum spectrum to be discussed in detail.

Chou, T. T.↗

NASA NTRS1985

Accelerated convergence for incompressible flow calculations

Neely, G. M.↗

NASA NTRS1985

A procedure for the calculation of supersonic flows with strong viscous-inviscid interaction

The present paper is concerned with the calculation of strong viscous-inviscid interactions in two-dimensional laminar supersonic flows with and without separation. The equations solved are the so-called parabolized Navier-Stokes equations. The streamwise pressure gradient term is written as a combination of a forward and a backward difference to provide a path for upstream propagation of information. Global iteration is utilized to repeatedly update the pressure field from an initial guess until convergence is achieved. The numerical scheme employed is a new alternating direction explicit (ADE) procedure which is used as an alternative to the more difficult to program multigrid strategy to accelerate convergence. Results are presented for flows past two flat plate related bodies.

Barnett, M.↗

NASA NTRS1983

The delayed energetic particle event of June 6-10, 1979

Energetic particle observations carried out with the ISEE-3 Medium-Energy Cosmic Ray experiment during the flare event of June 6-10, 1979 are reported. An expanded time history of the He nuclei particle spectra is given, and particle trajectory angles are identified with respect to the earth-sun line. The backward flow of the particle stream following the shock was analyzed, and it is found that the shock continued to accelerate particles beyond 1 AU from the sun. Polar plots of the number of protons counted in each sector of observation are given with their corresponding magnetic field directions.

Von Rosenvinge, T. T.↗

NASA NTRS1984

An elastic failure model of indentation damage

A mechanistically consistent model for indentation damage based on elastic failure at tensile or shear overloads, is proposed. The model accommodates arbitrary crack orientation, stress relaxation, reduction and recovery of stiffness due to crack opening and closure, and interfacial friction due to backward sliding of closed cracks. This elastic failure model was implemented by an axisymmetric finite element program which was used to simulate progressive damage in a silicon nitride plate indented by a tungsten carbide sphere. The predicted damage patterns and the permanent impression matched those observed experimentally. The validation of this elastic failure model shows that the plastic deformation postulated by others is not necessary to replicate the indentation damage of brittle structural ceramics.

Liaw, B. M.↗

NASA NTRS1984

Cosmogony as an extrapolation of magnetospheric research

A theory of the origin and evolution of the Solar System which considered electromagnetic forces and plasma effects is revised in light of information supplied by space research. In situ measurements in the magnetospheres and solar wind can be extrapolated outwards in space, to interstellar clouds, and backwards in time, to the formation of the solar system. The first extrapolation leads to a revision of cloud properties essential for the early phases in the formation of stars and solar nebulae. The latter extrapolation facilitates analysis of the cosmogonic processes by extrapolation of magnetospheric phenomena. Pioneer-Voyager observations of the Saturnian rings indicate that essential parts of their structure are fossils from cosmogonic times. By using detailed information from these space missions, it is possible to reconstruct events 4 to 5 billion years ago with an accuracy of a few percent.

Alfven, H.↗

NASA NTRS1985

On the accuracy of the pseudocompressibility method in solving the incompressible Navier-Stokes equations

The method of pseudocompressibility is being tested for its accuracy in solving the incompressible Navier-Stokes equations. An implicit, finite-difference computer code is used to solve the equations in a three-dimensional, curvilinear coordinate system. The code employs artificial compressibility for solving the pressure field, coupled with an implicit, approximate-factorization scheme. This coupling is known as the pseudocompressibility method. The pseudocompressibility method introduces pressure waves of finite speed into the fluid medium that would otherwise have an infinite sound speed. The waves die out as the solution converges, and the steady state solution approaches a divergence-free condition. However, these waves limit the time-accuracy of the computations. The effects of these waves are analyzed and criteria are set for choosing the pseudocompressibility parameters that govern the pressure wave speed. Test cases are presented that verify these criteria. The code is tested by computing laminar flow over a two-dimensional, backward-facing step and over a two-dimensional, impulsively started circular cylinder.

Rogers, S. E.↗